Calendar: 1870-1871 Page 510

510 GENERAL LITERATURE AND SCIENCE 18 Prove that the condition that the straight line 41 α β should be normal to the ellipse yl is a2 a2 β b2 19 Show that the condition that the pairs of lines ax2 hxy2 by2 r2 A0 י should form an harmonic pencil is b' -f 2hh' 20 In the conic aa ιίΐτ -f- iy2 find the locus of the middle points of series of chords drawn through given point 21 Find the polar reciprocal of circle with respect to conic one of whose foci coincides with its centre 22 conic is described touching the sides of the triangle of reference at the points where the lines β η meet the opposite sides prove that the normals at these points will meet in point if la TL- ft mp "ί 4- ne2 ί ί η η י 23 Explain how to determine the nature of any plane section of surface of the second order If the section of the surface whose equation is ax' by2 cz2 2a' yz b' xz xy a"χ b" c" by the plane my β be rect- angular hyperbola then will I2 2a'mn b' nl Zm Divisions II III Second Year -Divisions II III IV First Year II comrtrp If two angles of triangle be equal to one another the sides also which subtend the equal angles shall be equal to one another